Performance of normalized matched filters

In sonar or radar, the operation called normalization consists of getting a constant false alarm rate receiver by using a background noise power estimation to set the threshold. This study compares the performance of the two test functions obtained, in the white Gaussian noise case, by using two different maximum-likelihood noise power estimates, one under the hypotheses H₀ and the other under H₁. The latter has the noise-alone-reference (NAR) property, and the principal result is the quantification of the improvement in terms of deflection due to the use of the NAR estimation